If a long exposure is making the movement blurry rather than feeling like movement, maybe the only way to capture it is with short video clips
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DreamagerOct 9 '12 at 9:07

Are you sure the only thing moving in your pictures is the fog? What do you want to achieve? droplet trails?
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JahazielOct 9 '12 at 23:01

1

Yes, the objects themselves are not really blurred. The fog just turns into a blob when I've tried using long exposures, but doesn't feel like it's moving. Perhaps @DetlevCM is right and I just haven't found the right shutterspeed.
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RofloOct 10 '12 at 1:58

3 Answers
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I have not shot any such images myself - but immediately thought "long exposure".
Now given that you appear to know about the effects of long and short exposure, it might be an idea if you post some example images.

If you want any motion blur in an image that stems from the movement of objects in the image, the only way of achieving this is via a long exposure time.
Maybe you haven't found the right shutterspeed yet?

Given that a photograph is a single image of a slice of time (either a very short or very long slice), it will be difficult to show movement unless you can capture the edge of the fog wrapping around an object, or things moving in the fog.

Maybe a time-lapse would be perfect for what you want to achieve?

Have you seen examples of fog movement in images before? Maybe examining those examples will give you an insight on how to get the look you're after?